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刘木伙 (Muhuo Liu) 简历
华南农业大学,数学与信息(软件)学院,副教授,硕士研究生导师
男,1981年3月生,2014年于南京师范大学获理学博士学位,美国Mathematical Reviews评论员,主要从事结构图论和图谱理论等方面的研究,在《中国科学》、《J. Combin. Theory Ser. A》、《Adv. in Appl. Math.》《European J. Combin.》、《Electron. J. Combin.》、《Discrete Math.》、《Discrete Appl. Math.》、《Linear Algebra Appl.》、《Linear Multilinear Algebra》、《Graphs Combin.》等国内外数学学术刊物上发表或被接受科研论文90多篇,其中80多篇发表或被接受在SCI刊源期刊上。第一作者编写的专著《图谱的极值理论》于2017年由广东省科技出版社出版,其英文版于2018年由University of Kragujevac and Faculty of Science Kragujevac出版社出版。
      曾经参加或主持国家自然科学基金、国家自然科学青年基金、江苏省自然科学基金等项目的研究。于2010年入选华南农业大学青年骨干教师培养对象,2011年入选南京师范大学博士学术新人培养计划,2013年获博士研究生国家奖学金,2014年入选广东省高等学校“千百十人才培养工程”第八批校级培养对象,2015年入选广东省高等学校优秀青年教师培养计划。 

主持的课题:

(1)广东高校优秀青年创新人才培养计划项目(No. LYM10039,主持,3万): 图论的理论及其应用的研究,2011.01--2012.12;
(2)国家自然科学青年基金(11201156,主持,22万):图谱理论中若干问题的研究,2013.01-2015.12;
(3)2015年度广东省优秀青年教师培养计划(YQ2015027,主持,32万):对最小度有所约束的一些图的划分问题,2016.01—2018.12;
(4)广东省普通高校特色创新项目 (2017KTSCX020,主持,15万):图谱的优超理论,2018.01-2019.12. (5)广东省自然科学基金面上项目 (2022A1515011786,主持,10万):图谱确定性的研究,2022.01-2024.12.        
(6) 国家自然科学基金面上基金 (12271182,主持,46万 ):关于图结构的谱刻画问题的研究,2023.01-2026.12.

参与的课题:
(1) 广东省博士启动基金(No.5300084,排名第五,2万):组合矩阵论研究,2006.01—2007.12;
(2) 国家自然科学基金数学天元基金项目(No.10526019,排名第五,3万):组合数学-组合矩阵论研究,2006.01—2006.12;
(3)国家自然科学基金(No. 11071088,排名第三,25万),组合矩阵论的指数理论和谱理论,2011.01-2013.12;
(4)江苏省自然科学基金(No. BK20131357,排名第三,10万): 图的拓扑指标与图参数的极值问题及相关问题,2013.07-2016.06
(5)国家自然科学基金面上基金项目(No. 11571123,排名第三,50万):张量的本原性、本原指数及张量与超图谱若干问题的研究,2016/01-2019/12 

(I) 代表论文:
[1] M. Liu, H.-J. Lai, Kinkar Ch. Das,Spectral results on Hamiltonian problem,Discrete Math., 342 (2019) 1718-1730. (SCI)  
[2]Y. Yao, M. Liu (Corresponding author), Francesco Belardo, Chao Yang,Unified extremal results of topological indices and spectral invariants of graphs, Discrete Appl. Math., 271 (2019) 218–232. (SCI) [3]M. Liu, H. Shan, X. Gu, Spectral characterization of the complete graph removing a path, Discrete Appl. Math., 284 (2020) 499–512. (SCI)    
[4]M. Liu, X. Gu, Spectral characterization of the complete graph removing a path: Completing the proof of C\'amara-Haemers Conjecture, Discrete Math., 344(2021), 112-275.(SCI)     
[5] M. Liu, B.Xu, On a conjecture of Schweser and Stiebitz, Discrete Appl. Math., 295 (2021) 25–31. (SCI)  [6] M. Liu, C. Chen, Z. Stanić,On graphs whose second largest eigenvalue is at most 1,European J. Combin., 97 (2021) 103385 . (SCI)        
[7] B. Cheng, M. Liu (Corresponding author), B.-S. Tam, On the nullity of a connected graph in terms of order and maximum degree,Linear Algebra Appl., 632 (2022) 193– 232.(SCI)      
[8] M. Liu, B. Xu, On  connected partition with degree constraints, Discrete Math.,  345 (2022) 112680.(SCI)          
[9] M. Liu,X. Gu, Spectral strengthening of a theorem on transversal critical graphs, Discrete Math.,  345 (2022) 112717. (SCI)           
[10] X. Gu, M. Liu,A tight lower bound on the matching number of graphs via Laplacian eigenvalues,European J. Combin., 101 (2022) 103468.  (SCI)                                                             
 [11]M. Liu, C.Chen, Z. Stanić,Connected (K_4-e)-free  graphs  whose  second largest eigenvalue  does not exceed 1,European J. Combin., 115 (2024) 103775. (SCI)

[12] M.Liu, X. Gu, H.Shan, Z.Stanic, Spectral characterization of the complete graph removing a cycle, J. Combin. Theory Ser. A, 205 (2024), 105868. (SCI)  

[13] M. Zhai, M.Liu (Corresponding author), Extremal problems on planar graphs without k edge-disjoint cycles, Adv. in Appl. Math., 157 (2024) 102701. (SCI).   


(II) 其他的论文: 
 [1] B. Liu, Liu M.. On the spread of the spectrum of a graph,Discrete Math.,309 (2009),2727-2732. (SCI)
[2] M. Liu,B. Liu,Z. You, The majorization theorem of connected graphs,Linear Algebra Appl., 431(2009), 553-557. (SCI)
[3] M. Liu,B. Liu,The signless Laplacian spread, Linear Algebra Appl., 432(2010), 505-514. (SCI)
[4] M. Liu,B. Liu,On the k-th smallest and k-th greatest modified Wiener indices of trees,Discrete Appl. Math.,158 (2010), 699-705. (SCI)
[5] M. Liu, B. Liu,On the spectral radii and the signless Laplacian spectral radii of c-cyclic graphs with fixed maximum degree, Linear Algebra Appl., 435 (2011) 3045-3055. (SCI)
[6] M. Liu,The (signless Laplacian) spectral radii of connected graphs with prescribed degree sequences,Electron. J. Combin., 19(4) (2012), #P35 (SCI)
[7] M. Liu, Lihua You, Bolian Liu, The proof of a conjecture on the lewin number of primitive non-powerful signed digraphs, Linear Algebra Appl., 438 (2013), 2366-2377. (SCI).
[8] K.Ch. Das, K. Xu, M. Liu,On sum of powers of the Laplacian eigenvalues of graphs, Linear Algebra Appl., 439(2013), 3561-3575.(SCI)
[9] M. Liu, B. Liu,The second Zagreb indices of unicyclic graphs with given degree sequences,Discrete Appl. Math.,167 (2014), 217-221 .(SCI)
[10] M. Liu, H. Shan, K. Ch. Das, Some graphs determined by their (signless) Laplacian spectra, Linear Algebra Appl., 449(2014),154-165 (SCI).
[11] M. Liu, B. Liu,The majorization theorem of extremal pseudographs, Linear Algebra Appl., 459(2014), 13-22. (SCI)
[12] K. Ch. Das, M. Liu, H. Shan, Upper bounds on the (signless) Laplacian eigenvalues of graphs, Linear Algebra Appl., 459(2014),334-341. (SCI)
[13] M. Liu, B. Liu, B. Cheng, Ordering (signless) Laplacian spectral radii with maximum degrees of graphs, Discrete Math., 338 (2015), 159-163. (SCI)
[14] M. Liu, B. Xu, Bipartition of graph under degree constraints,Sci. China Math., 58(2015), 869–874. (SCI,《中国科学》英文版).
[15] K.Ch. Das,M. Liu,Complete split graph determined by its (signless) Laplacian spectrum,Discrete Appl. Math.,205(2016), 45-51.(SCI)
[16] H.Shan. M. Liu(Corresponding author), Laplacian spectral radius of c-cyclic graph and maximum vertex degree, Sci Sin Math, (46)2016, 1227–1240(中国科学(中文版)
[17] M. Liu, Y. Zhu, H. Shan, K. Ch. Das,The spectral characterization of butterfly-like graphs,Linear Algebra Appl., 513(2017),55-68.(SCI)
[18] M. Liu, K.Ch. Das,H. Lai,The spectral radii of c-cyclic graphs with n vertices, girth g and k pendant vertices,Linear Multilinear Algebra,65(2017),869-881. (SCI)
[19] G. Zhang,M. Liu, H. Shan, Which Q-cospectral graphs have same degree sequences, Linear Algebra Appl.,520(2017),274-285.(SCI)
[20] M.Liu, B. Xu,On partitions of graphs under degree constrains, Discrete Appl. Math., 226 (2017) 87-93.(SCI).
[21] M. Liu, Y.Yuan, L. You, Z. Chen, Which cospectral graphs have same degree sequences, Discrete Math., 341 (2018), 2969-2976. (SCI)
[22] M.Liu, K. Xu, X.-D. Zhang, Extremal graphs for vertex-degree-based invariants with given degree sequences,Discrete Appl. Math.,255 (2019) 267-277. (SCI)
[23] J. Ye, M. Liu(Corresponding author), Y. Yao, K.Ch. Das, Extremal polygonal cacti for bond Incident degree indices, Discrete Appl. Math.,257 (2019), 289-298. (SCI)
[24] B. Cheng, M. Liu(Corresponding author), Bolian Liu, Proof of a conjecture on the nullity of a connected graph in terms of order and maximum degree, Linear Algebra Appl., 587 (2020),291-301. (SCI)
[25] M. Liu, K.Cheng, I. Tomescu, Some notes on the extremal k-generalized quasi-unicyclic graphs with respect to Zagreb indices,Discrete Appl. Math., 284 (2020) 616–621. (SCI)
[26] M. Liu, I. Tomescu, J. Liu, Unified extremal results for $k$-apex unicyclic graphs (trees), Discrete Appl. Math., 288 (2021),35-49 (SCI).
[27] M. Liu, K. Cheng, B. Furtula, Minimum augmented Zagreb index of c-cyclic graphs, Discrete Appl. Math., 295 (2021) 32–38. (SCI) 
[28]C. Chen,  M. Liu(Corresponding author), X. Gu, K.C. Das,Extremal  augmented Zagreb index of trees with given numbers of vertices and leaves, Discrete Math., 345 (2022) 112753. (SCI)
[29] C.Chen, M. Liu(Corresponding author), X.Chen, W.Lin,On general ABC-type index of connected graphs, Discrete Appl. Math., 315 (2022) 27–35. (SCI)                                                                      
 [30] Y. Huang, M. Liu(Corresponding author), F. Belardo, The general spectral radii of (multicone-)graphs with prescribed degree sequence, Linear Multilinear Algebra, 70(2022), 4751–4777. (SCI)
[31]P. Wei, M. Liu(Corresponding author),Note on Sombor index of connected graphs with given degree sequence,Discrete Appl. Math., 330 (2023) 51–55. (SCI)                                                                
 [32]M. Liu, S.Pang, F.Belardoc, A.Ali,The k-apex trees with minimum augmented Zagreb index, Discrete Math., 346 (2023) 113390. (SCI)
[33] M. Liu, C.Chen, S.-G.Guo, J.Peng, T.Chen,The Aα-spectral radius of dense graphs,Linear  Multilinear Algebra,71(2023),1044–1053. (SCI)                                                                          
[34] P. Wei, M. Liu (Corresponding author), I.Gutman,On (exponential) bond incident degree indices of graphs, Discrete Appl. Math., 336 (2023) 141–147. (SCI)                                                                   
 [35] H. Shan, M. Liu, On the relationship between shortlex order and Aa-spectral radii of graphs with  starlike branch tree,Discrete Math.,347 (2024) 113772. (SCI)      

                                                                                                                                                
(III) 更多的SCI论文:

[1]M. Liu,B. Liu,Degree series of the 3-harmonic graphs,Appl. Math. J. Chinese Univ. 23(2008),481-489
[2] B. Liu, Z. Chen, Liu M., On graphs with largest Laplacian index,Czechoslovak Math. J. 58(4)(2008), 949-960.(SCI).
[3] B. Liu, Liu M., Z. You,Erratum to "A note on the largest eigenvalue of non-regular graphs",Electronic J. Linear Algebra,18 (2009), 64-68. (SCI)
[4] M. Liu,B. Liu,New sharp upper bounds for the first Zagreb index,MATCH Commun. Math. Comput. Chem., 62 (2009), 689-698. (SCI)
[5] Liu M., B. Liu, Trees with the seven smallest and fifteen greatest Hyper-Wiener indices, MATCH Commun. Math. Comput. Chem., 63(2010), 151-170. (SCI)
[6] M. Liu, A note on D-Equienergetic graphs, MATCH Commun. Math. Comput. Chem., 64(2010),135-140 (SCI)
[7] M. Liu, A simple approach to order the first Zagreb indices of connected graphs,MATCH Commun. Math. Comput. Chem., 63 (2010),425-432. (SCI)
[8] M. Liu,Bounds on the spectral radius of the line distance matrix,MATCH Commun. Math. Comput. Chem., 63(2010), 717-724 (SCI).
[9] M. Liu, B. Liu, Some results on the Laplacian spectrum spectrum, Comput. Math. Appl., 59 (2010), 3612-3616. (SCI,EI)
[10] M. Liu,B. Liu,Q. Li,Erratum to The trees on vertices with the first to seventeenth greatest Wiener indices are chemical trees',MATCH Commun. Math. Comput. Chem., 64 (2010), 743-756. (SCI)
[11] M.Liu,X. Tan, B.Liu,The (signless) Laplacian spectral radius of unicyclic and bicyclic graphs with n vertices and k pendant vertices,Czechoslovak Math. J.,60(3) (2010), 849-867. (SCI)
[12] M.Liu, B. Liu, On the variable Wiener indices of trees with given maximum degree, Math.Comput.Modelling, 52 (2010), 1651-1659. (SCI,EI)
[13] M. Liu,B.Liu,On the Wiener polarity index,MATCH Commun. Math. Comput. Chem., 66 (2011), 293-304 (SCI).
[14] M. Liu, B. Liu,F. Wei,Graphs determined by its (signless) Laplacian spectra, Electronic J. Linear Algebra, 22 (2011), 112-124. (SCI)
[15] M. Liu, B. Liu, A note on sum of powers of the Laplacian eigenvalues of graphs, Appl. Math. Lett., 24 (2011), 249-252 (SCI).
[16] M.Liu,B.Liu, The second Zagreb indices and Wiener polarity indices of trees with given degree sequences,MATCH Commun. Math. Comput. Chem., 67 (2012),439-450 (SCI)
[17] M.Liu, B.Liu, New method and new results on the order of spectral radius, Comput. Math. Appl., 63(2012) 679-686 (SCI,EI).
[18] M. Liu, B. Liu, Some results on the majorization theorem of connected gaphs,Acta Math.Sin.,Eng. Ser., 28 (2012),371-328.(SCI).
[19] M. Liu, B. Liu, Some results on the spectral radii of trees, unicyclic and bicyclic graphs, Electronic J. Linear Algebra,23 (2012),327-339 (SCI).
[20] M.Liu,Some graphs determined by their (signless) Laplacian spectra,Czechoslovak Math. J.,62(4) (2012), 1117-1134 (SCI).
[21] M.Liu, B.Liu, On sum of powers of the signless Laplacian eigenvalues of graphs, Hacet. J. Math. Stat., 41(4)(2012), 527-536 (SCI).
[22] M. Liu, The (signless) Laplacian spectrum of c-cyclic graphs with n vertices and k pendant vertices,Electronic J.Linear Algebra, 23(2012),942-952.(SCI)
[23] B. Liu, M. Liu, Z. You,The majorization theorem for signless Laplacian spectral radii of connected graphs, Graphs Combin., 29(2013),281-287.(SCI).
[24] M. Liu, F.Li, K.Ch. Das, Ordering the Zagreb coindices of connected graphs, MATCH Commun. Math. Comput. Chem., 70 (2013),939-948.(SCI)
[25] M.Liu, B.Liu, A note on the LEL-equienergetic graphs, Ars Combin., 113 (2014), 435-439 (SCI).
[26] H.Li, Y. Liang, M. Liu, B. Xu, On minimum balanced bipartitions of triangle-free graphs, J. Comb. Optim. 27 (2014), 557-566. (SCI).
[27] M. Liu, B.Liu, X. Tan, The first nine maximal LEL-invariant of graphs with n vertices, Util. Math., 93(2014), 153-160. (SCI)
[28] M.Liu, F. Wei, B.Liu,On the Laplacian spectral radii of tricyclic graphs,Ars Combin., 114(2014), 129-143. (SCI)
[29] M. Liu, B. Liu, The nine smallest hyper-Wiener indices of trees and the eight smallest Wiener (hyper-Wiener) indices of unicyclic graphs,Util. Math., 95 (2014): 129-139.(SCI)             [30] M. Liu, B.Liu, On the signless Laplacian spectra of bicyclic and tricyclic graphs,Ars Combin.,120(2015), 169-180. (SCI)
[31] I. Gutman, K. Xu, M.Liu, A congruence relation for Wiener and Szeged indices, Filomat, 29:5(2015),1081-1083. (SCI).
[32] M. Liu,B. Liu,R.Li,The strong pseudochromatic number of a graph, Util. Math.,98 (2015),3-21.(SCI)
[33] M. Liu, B.Xu, On judicious partitions of graphs,J. Comb. Optim.,31 (2016), 1383- 1398.(SCI).
[34] K.Ch. Das,M. Liu(Corresponding author),Quotient of spectral radius, (signless) Laplacian spectral radius and clique number of graphs,Czechoslovak Math.J.,66(2016), 1039–1048. (SCI)
[35] K. Ch. Das,M. Liu,Kite graphs determined by their spectra,Applied Math. Comput., 297(2017),74-78. (SCI)
[36] K.Ch. Das,M.Liu (Corresponding author),Minimal extremal graphs for addition of algebraic connectivity and independence number of connected graphs,Filomat,31(2017), 5545- 5551.(SCI)
[37] M.Liu, Y.Zhu, H.Shan, K.Ch. Das, Erratum to "The spectral characterization of butterfly-like graphs",Linear Algebra Appl., 539(2018), 274-276].(SCI)
[38] M. Liu,K.Ch. Das,On the ordering of distance-based invariants of graphs,Appl. Math. Comput., 324(2018),191-201. (SCI)
[39] K.Ch. Das,M.Liu,On two conjectures of spectral graph theory,Bull. Iran. Math. Soc. , 44(2018),43-51. (SCI)
[40] Y. Yao,M.Liu (Corresponding author),K.Ch. Das,Y.Ye,Some extremal results for vertex-degree-based invariants,MATCH Commun. Math. Comput. Chem.,81 (2019) 325-344. (SCI)
[41] Y.Yao, M. Liu, X.Gu,Unified extremal results for vertex--degree--based graph invariants with given diameter, MATCH Commun. Math. Comput. Chem.,82(2019), 699-714.(SCI)
[42] M.Liu,Y.Yuan,K.Ch. Das, The fan graph is determined by its signless Laplacian spectrum, Czechoslovak Math. J.,70 (2020), 21-31.(SCI)
[43] M.Liu, Y. Yao, K.Ch. Das,Extremal results for cacti, Bull. Malays. Math. Sci. Soc.,43(2020), 2783-2798. (SCI)
[44] M. Liu, G.Zhang, K.Ch. Das, Some properties of algebraic connectivity, Nation. Academy Sci. Lett., 43(2020), 537–542. (SCI)
[45] M. Liu, Y. Wu, H.-J. Lai,Unified spectral Hamiltonian results of balanced bipartite graphs and complementary graphs,Graphs Combin., 36(2020),1363-1390. (SCI)
[46] X. Tan, M. Liu(Corresponding author), J. Liu, On the Maximal General ABC Index of Graphs with Fixed Maximum Degree, MATCH Commun. Math. Comput. Chem., 85 (2021), 121-130. (SCI).
[47] K.Cheng,M.Liu,Fr.Belardo,The minimal augmented Zagreb index of k-apex trees for k {1,2,3},Appl. Math. Comput.,402(2021),126139. (SCI)
[48] M.Liu, K.C.Das, G.Zhang, The maximum number of spanning trees of a graph with given matching number, Bull. Malays. Math. Sci. Soc., 44 (2021) 3725–3732. (SCI)  
[49]W. Zhou, S. Pang, M. Liu,A. Ali,On bond incident degree indices of connected graphs with fixed order and number of pendent vertices, MATCH Commun. Math. Comput. Chem., 88 (2022), 625–642.  
[50]Y. Lan, P.Wei, M.Liu, C.Chen, Maximum and minimum Lanzhou index of c-cyclic graphs, MATCH Commun. Math. Comput.Chem., to appear. (SCI)


(IV) 发表的SCI综述:
[1] M.Liu, B.Liu, A survey on recent results of variable Wiener index,MATCH Commun. Math. Comput. Chem., 69(2013), 491-520. (SCI).
[2] K.Xu, M.Liu, K.Ch. Das, I.Gutman, B.Furtula, A survey on graphs extremal with respect to distance-based topological indices, MATCH Commun. Math. Comput. Chem.,71(2014), 461-508. (SCI).
[3] M.Liu, B.Liu, K.Ch. Das, Recent results on the majorization theory of graph spectrum and topological index theory-a survey, Electronic J.Linear Algebra, 30(2015), 402-421. (SCI).

(V) 学术会议与学术交流:
[1] 2012年7月15日至2012年7月19日,洛阳,第五届全国组合数学与图论大会:Spectral radius and maximum degree
[2] 2013年5月30日至6月2日,福州,图与超图谱理论国际研讨会议:The Theory and Application of the Majorization Theorems
[3] 2013年7月17日至7月21日,韩国成均馆大学,韩国水原市:The Theory and Application of the Majorization Theorems
[4] 2013年7月28日至7月31日,青海省西宁市:International Conference on Algebric Graph Theory and its Applications:The (signless) Laplacian spectral radii of c-cyclic graphs with n vertices and k pendant vertices
[5] 2014年11月8日至11月10日,广州,第六届全国组合数学与图论大会: 对最小度有所约束的图的划分问题
[6] 2015年07月18日至07月19日,兰州,第六届图论与组合算法国际研讨会(GTCA2015):Some results on judicious k-partitions of graphs
[7] 2016年 4月8至9日, Wright State University, Dayton, MIGHTY LVII (57th MIdwest GrapH TheorY Meeting,The (signless) Laplacian spectral radii of c-cyclic graphs with n vertices, girth g and k pendant vertices
[8] 2016年12月17日至18日,湖南长沙,长沙·2016代数图论及其应用研讨会:谱半径排序的统一方法和统一结果
[9] 2017年11月11月3日至11月5日,福州,第九届海峡两岸图论与组合数学学术会议
[10] 2017年11月15日,暨南大学, 报告题目:谱半径排序的统一方法和统一结果
[11] 2017年12月4日,华南师范大学,报告题目:谱半径排序的统一方法和统一极图
[12] 2018年1月8日,中山大学,报告题目:Some results on partition problem of graphs
[13] 2018年1月16日,南京航空航天大学理学院,报告题目:The majorization theory and its application
[14] 2018年2月27日,韩国成均馆大学,报告题目:The majorization theory and its application
[15] 2018.07.06-2018.07.08,珠海中山大学,广东省组合图论学术会议,报告题目:Unified methods and results on the spectral property of hamiltonian problem
[16] 2018.08.23-2018.08.27,合肥,第八届全国组合数学与图论大会,报告题目:Unified methods and results on the spectral property of hamiltonian problem
[17] 2018年10月12日-14日,山东理工大学,2018图论及其应用研讨会,报告题目:Unified extremal results of topological index and graph spectrum
[18] 2018年10月26日-28日,河海大学,2018南京图论及其应用研讨会,报告题目:Which degree sequence is determined by its graph spectrum
[19] 2018年12月21日-22日,浙江理工学院,2018杭州图论及其应用研讨会,报告题目:Unified extremal results of topological index and graph spectrum
[20] 2019年2月20日-25日,韩国成均馆大学,报告题目:Unified extremal results of topological index and graph spectrum.
[21] 2019年9月20日-24日,河南理工工大学,2019年代数组合国际研讨会,报告题目:The majorization theory of graph spectrum,
[22] 2019年11月20-24日,佛山, 中国数学会第十三次全国会员代表大会.
[23] 2019年12月6日-8日,安徽大学,第三届合肥图与组合前沿进展研讨会,报告题目:Some partition problems of graphs with minimum degree condition。
[24] 2019年12月16日,广州民航,2019年广航院组合数学与图论学术交流报告会.
[25] 2020年10月31日,华南理工大学,Unified methods and results on the spectral property of hamiltonian problem. 
[26] 2020年11月28日,上海同济大学,Some results on DS-graphs. 
[27] 2021年4月16-19日,滁州学院,第九届矩阵与图谱理论研讨会,On graphs whose second largest eigenvalue is at most 1

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